CN114179522A

CN114179522A - Reducing dimensional changes in funnel nozzles

Info

Publication number: CN114179522A
Application number: CN202111351926.1A
Authority: CN
Inventors: G.德布拉班德; M.内波尼什
Original assignee: Fujifilm Dimatix Inc
Current assignee: Fujifilm Dimatix Inc
Priority date: 2017-02-23
Filing date: 2018-02-22
Publication date: 2022-03-15
Anticipated expiration: 2038-02-22
Also published as: WO2018156753A1; JP2020509948A; EP4129693A3; CN110461610B; US20180236771A1; US11571895B2; US20180326729A1; US10052875B1; US10850518B2; JP7001698B2; US20230133379A1; US20210031521A1; JP7475513B2; EP4129693A2; JP7242826B2; EP3585618A1; EP3585618A4; JP2023065675A; US20200070518A1; CN110461610A

Abstract

Techniques for fabricating a funnel-shaped nozzle in a substrate are provided. The method can comprise the following steps: forming a first opening having a first width in a top layer of a substrate; forming a patterned layer on the top surface of the substrate, the patterned layer including a second opening having a second width greater than the first width; reflowing the patterned layer to form curved side surfaces terminating at a top surface of a substrate; a second layer of the substrate is etched through a first opening in a top layer of the substrate to form a straight-walled recess having a first width and a side surface substantially perpendicular to a top surface of the substrate.

Description

Reducing dimensional changes in funnel nozzles

The present application is a divisional application of the application with application number 201880020759.2 entitled "reducing dimensional changes of funnel nozzle" filed on 2018, 2 and 22.

Technical Field

This description relates to nozzle formation in microelectromechanical devices such as inkjet printheads.

Background

Printing high quality, high resolution images with inkjet printers typically requires that the printer accurately eject a desired amount of ink at a specified location on the print medium. Typically, a plurality of densely packed ink ejection devices are formed in a printhead structure, each including a nozzle and an associated ink flow path. The ink flow path connects an ink storage unit (e.g., an ink reservoir or cartridge) to the nozzle. The ink flow path includes a pumping chamber. In the pumping chamber, the ink may be pressurized to flow toward a drop zone terminating in a nozzle. Ink is discharged from an opening at the end of the nozzle and lands on the print medium. The medium is movable relative to the fluid ejection device. Ejection of a fluid drop from a particular nozzle is synchronized with movement of the media to place the fluid drop at a desired location on the media.

Various processing techniques may be used to form the ink ejectors in the printhead structure. These processing techniques may include layer formation, such as deposition and bonding, and layer modification, such as etching, laser ablation, punching and cutting. The technique used may vary depending on the desired nozzle shape, flow path geometry, and materials used in, for example, an inkjet printer.

Disclosure of Invention

A funnel shaped nozzle is disclosed having a straight walled bottom and a curved top. The curved top of the funnel-shaped nozzle converges gradually towards the bottom of the straight wall and connects smoothly therewith. The funnel-shaped nozzle may have one or more side surfaces around the axis of symmetry, and the cross-sections of the curved top and the straight-walled bottom in a plane perpendicular to the axis of symmetry are geometrically similar. In addition, the curved top of the funnel encloses a much larger volume than the straight wall bottom, which has sufficient height to maintain the straightness of the spray of fluid droplets sprayed through the funnel.

To manufacture the funnel-shaped nozzle described in this specification, first, a uniform photoresist layer is deposited on the dielectric coated surface of the semiconductor substrate. The dielectric may be thermally grown silicon dioxide and the substrate may be a silicon-on-insulator wafer. The photoresist layer is patterned using UV exposure and then resist development is performed. The cross-sectional shape of the smallest dimension of the nozzle may resemble the opening in the resist, allowing oval, circular and arbitrary nozzle shapes. Dry etching is used to transfer the opening in the resist into the dielectric and strip the resist.

The uniform photoresist layer is similarly patterned with an opening having one or more sidewalls that are substantially perpendicular to the planar top surface of the semiconductor substrate and the planar top surface of the photoresist layer. The resist opening is designed to be slightly larger, have a similar shape, and be precisely aligned with the opening in the dielectric. The patterned photoresist layer is then heated in a vacuum such that the photoresist material in the layer softens and reflows under the influence of the surface tension of the photoresist material. As a result of the backflow, the oblique corners on or between the top edges of the openings are rounded and the top edges transition into a single rounded edge. The radius of curvature of the rounded edge can be controlled by reflow baking conditions. For example, the radius of curvature of the rounded edge may be equal to or greater than the initial thickness of the uniform photoresist layer deposited on the semiconductor substrate. After the desired rounded shape of the top edge is achieved, the patterned photoresist layer is allowed to cool and re-harden while maintaining the rounded shape of the top edge. After reflow, the resist layer that is opened at the dielectric interface remains slightly larger than the opening in the dielectric.

After forming the patterned photoresist layer having the opening with the curved side surface gradually expanding toward and smoothly connecting with the exposed top surface of the patterned photoresist layer, the formation of the funnel-shaped recess in the semiconductor substrate may start.

A straight-walled recess is etched into the semiconductor substrate through an opening defined by the dielectric layer, rather than an opening formed by a reflowed photoresist layer. For example, a straight-walled recess may be formed using a Bosch process. The highly selective etching of the straight-walled recess leaves the photoresist layer substantially unetched. The depth of the recess may be a few microns less than the final design length of the funnel. Once the straight-walled recesses are formed into the semiconductor substrate, the straight-walled recesses are transformed into funnel-shaped recesses using an isotropic dry etching process. In particular, for the materials of the photoresist, dielectric, and semiconductor substrate (e.g., Si <100> wafers), the etchant used in the dry etch should have comparable (e.g., substantially equal) etch rates. During dry etching, the straight-walled recesses are gradually deepened by the etchant to form straight-walled bottoms of funnel-shaped recesses. Meanwhile, the dry etching expands the sidewall of the hole portion in the vicinity of the dielectric layer into a curved side surface, which extends flatly into the horizontal surface of the semiconductor substrate. The funnel converges towards and smoothly transitions to the straight-walled bottom of the funnel-shaped recess. The funnel-shaped recess can be opened at the bottom by removing the unetched substrate from below.

In one aspect, a method of manufacturing a nozzle, the method comprising: forming a first opening having a first width in a top layer of a substrate; a patterned photoresist layer is formed on the top surface of the substrate, the patterned photoresist layer including a second opening having a second width greater than the first width. The method comprises the following steps: reflowing the patterned photoresist layer to form curved side surfaces that terminate at the top surface of the substrate; a second layer of the substrate is etched through a first opening in a top layer of the substrate to form a straight-walled recess having a first width, a bottom surface, and a side surface substantially perpendicular to a top surface of the semiconductor substrate.

After forming the straight-walled recess, the method includes dry etching the curved side surface of the patterned photoresist layer, the top layer of the substrate, and the second layer of the substrate, wherein the dry etching i) transforms the straight-walled recess into a funnel-shaped recess, the funnel-shaped recess including curved sidewalls that gradually and smoothly connect lower portions of the straight walls of the recess or terminate at the bottom surface, ii) expands a portion of the straight-walled recess to a third width that is greater than the first width, and iii) expands the first opening in the top layer to a fourth width that is greater than the third width.

Implementations may include one or more of the following features. The second opening may be about 1 μm larger than the first opening. A stepper may be used to precisely align the patterned photoresist layer on the top surface of the substrate having the first opening. The first opening may be formed by etching with a thin, unrecirculated resist. The substrate may be a semiconductor substrate and the first layer may be an oxide layer having a high selectivity to the Bosch etch process. A portion of the fourth width may be 40 μm greater than the first width. Reflowing the patterned photoresist layer may include softening the patterned photoresist layer by heating until a top edge of the second opening becomes rounded under the influence of surface tension. After softening by heating, the patterned photoresist layer may be re-hardened while the top edge of the second opening remains rounded.

The patterned photoresist layer deposited on the top surface of the substrate may have a thickness of at least 10 microns. Softening the patterned photoresist layer by heating may further include heating the patterned photoresist layer having the second opening formed therein in a vacuum environment until the photoresist material in the patterned photoresist layer reflows under the influence of surface tension. Heating the patterned photoresist layer may include heating the patterned photoresist layer to a temperature of 160-250 degrees celsius. Re-hardening the patterned photoresist layer may include cooling the patterned photoresist layer while the top edge of the second opening remains rounded. The width of the top opening of the curved top may be at least four times the width of the bottom opening of the curved top. Etching the top surface of the substrate to form the straight-walled recess may include etching the top surface of the semiconductor substrate through an opening in the patterned photoresist layer using a Bosch process.

The dry etch forming the funnel-shaped recess may have substantially the same etch rate for the patterned photoresist layer and the semiconductor substrate. The dry etching to form the funnel-shaped recess may include dry etching using a CF4/CHF3 gas mixture. The first opening in the patterned photoresist layer may have a circular cross-sectional shape in a plane parallel to the exposed top surface of the patterned photoresist layer. The funnel-shaped recess may have a circular cross-sectional shape in a plane parallel to the top surface of the substrate. The standard deviation of the nozzle widths of the plurality of nozzles may be less than 0.15 microns. The recess may extend all the way through the top layer.

Particular implementations may include none, one, or more of the following advantages.

The funnel-shaped nozzle has a curved top with a volume large enough to accommodate several droplets (e.g., 3 or 4 droplets) of fluid. The lateral surfaces of the funnel-shaped nozzle are streamlined and have no discontinuities in the fluid ejection direction. The side surfaces of the funnel-shaped nozzle create less friction on the fluid during fluid ejection than a straight-walled nozzle (e.g., a cylindrical nozzle) of the same depth and droplet size, and prevent the nozzle from drawing air when the droplets break off from the nozzle. Reducing fluid friction not only improves the stability and uniformity of droplet formation, but also allows for higher ejection frequencies, lower drive voltages, and/or higher power efficiencies. A single narrow portion with a nozzle may hold the meniscus in a stable position. Preventing air from entering the nozzle helps prevent trapped air bubbles from clogging the nozzle or other portions of the flow path.

While nozzles having tapered flat sidewalls (e.g., inverted pyramid shaped nozzles) may also achieve some advantages (e.g., reduced friction) over cylindrical nozzles, the sharp-angled edges at the bottom opening of the tapered nozzle still cause greater resistance to liquid droplets than the funnel shaped nozzles. In addition, the slanted edges and rectangular (or square) shape of the tapered nozzle opening also affect the straightness of the drop direction in an unpredictable manner, resulting in degradation of print quality. In the funnel-shaped nozzles described in this specification, the straight-walled bottom does not occupy the entire nozzle depth or a small portion thereof, and therefore the straight-walled bottom ensures the straightness of the spray without causing too much friction to the discharged fluid. Thus, the funnel-shaped nozzle may help achieve better jet straightness, higher exit frequency, higher power efficiency, lower drive voltage, and/or uniformity of droplet shape and position.

Although a funnel-shaped nozzle having curved side surfaces may be formed using electroforming or micromolding techniques, such techniques are limited to metal or plastic materials and may not be suitable for forming nozzles in semiconductor substrates. In addition, electroforming or micromolding techniques tend to have less precision and are not able to achieve the size, geometry and spacing requirements required for high resolution printing. Semiconductor processing techniques can be used to produce large nozzle arrays that are highly compact and uniform, and can meet the size, geometry, and spacing requirements required for high resolution printing. For example, the nozzle may be as small as 5 microns, the nozzle-to-nozzle spacing accuracy may be about 0.5 microns or less (e.g., 0.25 microns), the first nozzle-to-last nozzle spacing accuracy may be about 1 micron, and the nozzle size accuracy may be at least 0.6 microns.

The methods and systems disclosed herein reduce variations in funnel bore diameter. Reduced nozzle size variation can reduce (e.g., eliminate) printing line width variation and reduce the need to discard nozzle plates containing nozzles with too much variation. Since the dimensional variations are less pronounced in straight holes etched into silicon wafers using non-reflowed resist, the methods disclosed herein use the edges of the openings in the oxide layer, rather than the openings in the reflowed photoresist, to define the dimensions of the Bosch-etched straight-walled recesses, which are precursors to the funnel-shaped nozzles. By making the oxide opening slightly smaller than the photoresist opening, the oxide rather than the reflowed resist allows the opening to be made with a thin, unrecirculated resist, so the oxide opening is more accurate than the reflowed resist opening. The oxide also has a high selectivity to Bosch etching. The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.

Drawings

Fig. 1 shows a cross-sectional side view of a device for fluid droplet ejection.

Fig. 2A is a cross-sectional side view of a printhead flow path with a nozzle having a single straight sidewall (i.e., a cylindrical nozzle) and a top view of the nozzle.

FIG. 2B is a cross-sectional side view of a printhead flow path with a nozzle having tapered flat sidewalls and a top view of the nozzle.

Fig. 2C is a cross-sectional side view of a printhead flow path with a nozzle having a tapered top portion protrudingly connected to a straight-walled bottom portion and a top view of the nozzle.

Fig. 3A is a cross-sectional side view of a funnel-shaped nozzle with a curved top smoothly connected to a straight-walled bottom.

Fig. 3B is a top view of a funnel-shaped nozzle with a curved top smoothly connected to a straight-walled bottom, wherein the horizontal cross-sectional shape of the nozzle is circular.

Fig. 3C is a cross-sectional side view of a printhead flow path with nozzles having tapered tops smoothly connected to straight-walled bottoms.

Fig. 4A-4F illustrate a process of manufacturing a funnel-shaped nozzle with a curved top smoothly connected to a straight-walled bottom.

Fig. 5A and 5B show images of funnel-shaped recesses made using the process shown in fig. 4A-4F.

Fig. 6A and 6B compare the maximum, minimum and average nozzle sizes of nozzles made using the process shown in fig. 4A-4F and another process.

Fig. 7A and 7B compare the standard deviation of nozzle sizes for nozzles made using the process shown in fig. 4A-4F with another process.

Like reference symbols in the various drawings indicate like elements.

Detailed Description

Fluid droplet ejection can be achieved with a substrate, such as a microelectromechanical system (MEMS), including a fluid flow body, a membrane, and a nozzle layer. The flow path body has a fluid flow path formed therein, which may include a fluid filling channel, a fluid pumping chamber, a descender, and a nozzle having an outlet. The actuator may be located on a surface of the membrane opposite the flow path body and proximate the fluid pumping chamber. When the actuator is actuated, the actuator applies a pressure pulse to the fluid pumping chamber to eject a fluid droplet through the outlet of the nozzle. Typically, the flow path body comprises a plurality of fluid flow paths and nozzles, such as a densely packed array of identical nozzles and their respective associated flow paths. A fluid droplet ejection system can include a substrate and a fluid source for the substrate. The fluid reservoir may be fluidly connected to the substrate for supplying fluid for ejection. The fluid may be, for example, a chemical compound, a biological substance, or an ink.

Referring to FIG. 1, a schematic cross-sectional view of a portion of a micro-electromechanical device, such as a printhead in one embodiment, is shown. The printhead includes a substrate 100. The substrate 100 includes a fluid path body 102, a nozzle layer 104, and a membrane 106. The nozzle layer 104 is made of a semiconductor material such as silicon. The fluid reservoir supplies fluid to the fluid-filled passage 108. The fluid-filled passage 108 is fluidly connected to a riser 110. The riser 110 is fluidly connected to a fluid pumping chamber 112. The fluid pumping chamber 112 is proximate to the actuator 114. Actuator 114 may include a piezoelectric material, such as lead zirconate titanate (PZT), interposed between a drive electrode and a ground electrode. A voltage may be applied between the drive electrode and the ground electrode of the actuator 114 to apply a voltage to the actuator to actuate the actuator. The membrane 106 is located between the actuator 114 and the fluid pumping chamber 112. An adhesive layer (not shown) may secure the actuator 114 to the membrane 106.

The nozzle layer 104 is secured to the bottom surface of the fluid path body 102 and may have a thickness between about 15 and 100 microns. A nozzle 117 having an outlet 118 is formed in an outer surface 120 of the nozzle layer 104. The fluid pumping chamber 112 is fluidly connected to a descender 116, which is fluidly connected to a nozzle 117.

Although fig. 1 shows individual channels, such as fluid-filled channels, pumping chambers, and descenders, these components may not all be in a common plane. In some embodiments, two or more of the fluid path body, the nozzle layer, and the membrane may be formed as a unitary body. In addition, the relative sizes of the components may vary, and the size of some of the components is exaggerated in FIG. 1 for illustrative purposes.

The design of the flow path, particularly the nozzle size and shape, affects print quality, print resolution, and energy efficiency of the printing device. Fig. 2A-2C illustrate a number of conventional nozzle shapes.

For example, fig. 2A shows a printhead flow path 202 having straight nozzles 204. The straight nozzle 204 has straight sidewalls 206. The top of fig. 2A shows a cross-sectional side view of the nozzle 204 and the flow path 202 in a plane passing through a central axis 208 of the nozzle 204. The central axis 208 is an axis passing through the geometric center of all horizontal cross-sections of the nozzle 204. In this description, the central axis 208 of the nozzle is sometimes referred to as the symmetry axis of the nozzle, in the case where the geometric center of each horizontal cross-section is also the center of symmetry of the horizontal cross-section. As shown at the top of fig. 2A, in a plane including the central axis 208, the profile of the sidewall 206 is a straight line parallel to the central axis 208. In this example, the nozzle 204 is circular, straight cylindrical and has a single, straight sidewall. In other examples, the nozzle may be square, right cylindrical and have four straight, flat side surfaces.

As shown in fig. 2A, the nozzles 204 are formed in a nozzle layer 210. The nozzles 204 have the same cross-sectional shape and size in a plane perpendicular to a central axis 208 of the nozzles 204. The lower portion of fig. 2A shows a top view of the nozzle layer 210. In this example, the nozzle 204 has a circular cross-sectional shape in a plane perpendicular to a central axis 208 of the nozzle 204. In various embodiments, the nozzle 204 may have other cross-sectional shapes, such as oval, square, rectangular, or other regular polygonal shapes.

Nozzles with straight sidewalls are relatively easy to manufacture. The straight sidewalls of the nozzle can help maintain jetting straightness and make the landing position of the ink drop jetted from the nozzle more predictable. However, in order to ensure a sufficient droplet size, the height of the straight-wall nozzle needs to be considerably large (e.g., several tens of micrometers or more). The large vertical dimension of the straight-walled nozzle creates a large amount of friction on the fluid within the nozzle as the fluid is ejected from the nozzle as droplets. The higher flow resistance created in straight-walled nozzles results in lower firing frequencies and/or higher drive voltages, which may further result in lower print speeds, lower resolution, lower power efficiency, and/or lower device lifetime.

Another disadvantage of straight wall nozzles is that when liquid droplets break off from the outlet of the nozzle (e.g., outlet 212), air may be drawn into the nozzle from the outlet opening of the nozzle and become trapped within the nozzle or other portion of the flow path. Air trapped within the nozzle can block the ink flow or deflect fluid droplets ejected from their desired trajectory.

Fig. 2B shows a printhead flow path 214 with a nozzle 216 having a tapered planar sidewall 218. The upper portion of fig. 2B shows a cross-sectional side view of the printhead flow path 214 in a plane containing the central axis 220 of the nozzle 216. In a plane containing central axis 220, the profile of nozzle 216 is a straight line that converges toward central axis 220 from the top opening of nozzle 216 to the bottom opening (or outlet 212) of nozzle 216. The profile of nozzle 216 may be formed by a plurality of planes that converge toward central axis 220.

Nozzles 216 are formed in nozzle layer 224, and the cross-sectional shape of nozzles 216 in a plane perpendicular to central axis 220 is a continuously decreasing size square. Nozzle 216 has four flat sidewalls, each of which slopes from an edge of the top opening of nozzle 216 to a corresponding edge of the bottom opening of nozzle 216. The lower portion of fig. 2B shows a top view of the nozzle layer 224. As shown in the lower portion of fig. 2B, each sidewall 218 of nozzle 216 is a flat surface that intersects each of two adjacent flat sidewalls 218 along an edge 226. Each edge 226 is a beveled edge rather than a rounded edge.

As shown in the lower portion of fig. 2B, the lower opening of nozzle 216 is a smaller square opening, while the upper opening of nozzle 216 is a larger square opening. The central axis 220 passes through the geometric center of the upper and lower openings of the nozzle 216. The tapered sidewall 218 of the nozzle 216 provides reduced friction to the fluid passing through the nozzle as compared to the straight-walled nozzle 204 shown in fig. 2A. The conical shape of nozzle 216 also reduces the amount of air intake that occurs during droplet break-up at nozzle outlet 212.

The tapered nozzle 216 shown in fig. 2B may be formed in a semiconductor nozzle layer 224 (e.g., a silicon nozzle layer) by using KOH etching. However, the shape of the tapered nozzle 216 is determined by the crystal planes present in the semiconductor nozzle layer 224. When the nozzle 216 is formed by KOH etching, the side surface of the nozzle 216 is formed along the <111> crystal plane of the semiconductor nozzle layer 224. Thus, the angle between each inclined side surface 218 and the central axis 220 has a fixed value of about 35 degrees.

While the tapered nozzle 216 shown in FIG. 2B provides some improvement over the straight-walled nozzle 204 shown in FIG. 2A in terms of reduced flow resistance and reduced air absorption, there is very little flexibility in changing the shape of the nozzle opening or the angle of the tapered sidewalls. The square angle of the nozzle outlet sometimes forms satellites (creating tiny secondary droplets in addition to the primary droplets during droplet ejection). In addition, the sharp discontinuity between the flat sidewall 218 at the edge of the nozzle outlet 212 and the horizontal bottom surface of the nozzle layer 224 also causes additional drag on the droplets, resulting in reduced ejection speed and frequency.

FIG. 2C shows another nozzle configuration that combines a tapered portion as shown in FIG. 2B with a straight portion as shown in FIG. 2A. Due to limitations of KOH etching techniques, straight bottom portions and tapered top portions are formed by etching from both sides of the substrate. However, double-sided etching can lead to difficult alignment issues. In addition, specially designed steps must be taken to form the straight bottom from the same side as the tapered portion, such as described in U.S. patent publication 2011-.

The top of fig. 2C shows a cross-sectional side view of the printhead flow path 232 with a nozzle 234 having a tapered top 236 protrudingly connected to a straight bottom 238. The cross-sectional side view shown in FIG. 2C lies in a plane containing the central axis 240 of the nozzle 234. In a plane containing the central axis 240, the profile of the conical top 236 includes straight lines that converge from the top opening of the nozzle 234 toward the intersection between the conical top 236 and the straight-walled bottom 238. In a plane containing the central axis 240, the profile of the straight-walled bottom 238 includes a straight line parallel to the central axis 240. The profile may be provided by a cylinder coaxial with the central axis 240. The intersection between the tapered top 236 and the straight bottom 238 is not smooth and has one or more discontinuous or sloped edges in the vertical direction (i.e., the fluid ejection direction in this example).

In this example, the cross-sectional shape of the conical top 236 in a plane perpendicular to the central axis of the nozzle 234 is square, while the cross-sectional shape of the bottom 238 in a plane perpendicular to the central axis of the nozzle 234 is circular. Thus, the tapered top 236 has four flat side surfaces 244, each sloping from the edge of the top opening of the tapered top 236 to the corresponding edge of the intersection between the top 236 and the bottom 238. Although the straight bottom 238 shown in FIG. 2C has a circular cross-section, the straight bottom may have a square cross-section or other cross-section.

The nozzles 234 are formed in the nozzle layer 242. The lower portion of fig. 2C shows a top view of the nozzle 234. In this top view, the lower opening of the straight-walled bottom 238 is circular and the top opening of the tapered top 236 is square, and the intersection between the straight bottom 238 and the tapered top 236 is the intersection between a cylindrical hole and an inverted pyramid hole. The intersecting edges include curves and sharp discontinuities due to the mismatch between the cross-sectional shapes of the top and bottom portions. These discontinuities can also cause fluid friction and instability in droplet formation. Even if the cross-sectional shapes of the top 236 and bottom 238 are both square, there is a discontinuity at the intersection between the two portions in the direction of fluid ejection. A square nozzle opening is also less desirable than a round nozzle outlet for other reasons such as described with respect to fig. 2B.

In this specification, a funnel-shaped nozzle having a curved top smoothly connected to a straight-walled bottom formed in a semiconductor nozzle layer (e.g., a silicon nozzle layer) is disclosed. The curved top of the funnel-shaped nozzle differs from the conical top shown in fig. 2C in that the profile of the side surface of the curved top in the plane containing the central axis of the nozzle is constituted by a curved line instead of a straight line. In addition, the profile of the curved top converges toward and smoothly connects to the straight-walled bottom, rather than curving at an abrupt angle at the intersection between the curved top and the straight-walled bottom.

In addition, in some embodiments, the transition from the horizontal top surface of the nozzle layer to the curved side surface of the funnel-shaped nozzle is also smooth rather than abrupt. In addition, the horizontal cross-sectional shape of the funnel-shaped nozzle in a plane perpendicular to the central axis of the nozzle is geometrically similar and concentric for the entire depth of the nozzle. Thus, there is no jagged intersection between the curved top of the funnel and the straight wall bottom. The funnel-shaped nozzle described in this specification provides a number of advantages over conventional nozzle shapes such as described with respect to fig. 2A-2C.

Fig. 3A is a cross-sectional side view of a funnel-shaped nozzle 302 having a curved top 304 smoothly connected to a straight-walled bottom 306. In the straight-walled base 306, the sides of the nozzle are parallel and perpendicular to the outer surface 322 of the nozzle layer. The straight-walled bottom 306 may be a cylindrical channel (i.e., the walls are straight up/down rather than in the transverse direction). Depending on the processing parameters, straight wall portion 306 may be avoided and funnel portion 316 may continue to surface 322. The funnel-shaped nozzle 302 is a funnel-shaped through hole formed in the planar semiconductor nozzle layer 308. The intersection between the curved top 304 and the straight-walled bottom 306 (the location of which is indicated by dashed line 320 in fig. 3A) is smooth and substantially free of any discontinuities and any surfaces perpendicular to the central axis 310 of the nozzle 302.

As shown in fig. 3A, the height of curved top 304 is substantially greater than the height of straight-walled bottom 306. However, the straight-walled bottom 306 may have at least some height, such as 10-30% of the height of the curved top 304. For example, the height of the curved top 304 may be 40-75 microns (e.g., 40, 45, or 50 microns) while the height of the bottom 306 may be only 5-10 microns (e.g., 5, 7, or 10 microns). The curved top 304 encloses a much larger volume than the straight-walled bottom 306. The larger curved top portion holds most of the fluid to be ejected. In some embodiments, the volume enclosed in the curved top 304 is the size of a number of droplets (e.g., 3 or 4 droplets). Each droplet may be 3-100 picoliters. The straight bottom portion 306 has a smaller volume, such as having a volume less than the size of a single droplet.

The height of the straight wall portion 306 is small enough that it does not cause a significant amount of fluid friction and does not cause a significant amount of air absorption during drop break-off. Meanwhile, the height of the straight wall portion is large enough to maintain the ejection straightness. In some embodiments, the height of the straight wall portion 306 is about 10-30% of the nozzle outlet diameter. For example, in FIG. 3A, the diameter of the nozzle outlet is 35 microns and the height of the straight wall portion is 5-10 microns (e.g., 7 microns). In some embodiments, the diameter of the nozzle outlet may be 15-45 microns.

Both the curved top 304 and the straight-walled bottom 306 of the nozzle 302 play an important role in droplet formation and ejection. The curved roof 304 is designed to hold a sufficient volume of fluid such that when a droplet is ejected from the nozzle outlet, little or no void is created in the nozzle to form a bubble within the nozzle. The bottom of the funnel can hold a small volume of fluid.

The funnel-shaped nozzle 302 also differs from the nozzles shown in fig. 2B and 2C in that the cross-sectional shape of the funnel-shaped nozzle 302 in a plane perpendicular to the central axis 310 of the nozzle 302 is circular rather than rectangular for the entire depth of the nozzle 302. Thus, there is no discontinuity between the curved top 304 and the straight bottom 306 in the fluid ejection direction. The streamlined profile of the funnel-shaped nozzle 302 provides even less fluid friction than the nozzles shown in fig. 2B and 2C. In addition, the side surfaces of the funnel-shaped nozzle 304 are completely smooth and also free of any discontinuities or abrupt changes in azimuthal direction. Accordingly, the funnel-shaped nozzle 304 also does not create drag or instability that can lead to other disadvantages (e.g., satellite formation) that may be present in the nozzles shown in fig. 2B and 2C.

Forming a funnel-shaped nozzle in silicon using conventional etching processes can be difficult. Conventional etching processes such as the Bosch process form straight vertical walls, while the KOH etch forms tapered straight walls. Although isotropic etching can form curved features, such as bowl-shaped features, curved walls cannot be made in the opposite formation to form funnel-shaped features.

In addition, in view of the processing techniques provided in this specification, the spacing at which the curved top of the funnel-shaped nozzle converges from its top opening towards the bottom of the straight wall may be varied by design, rather than fixed by the orientation of certain crystal planes. Specifically, assume that point a is the intersection between the edge of the top opening of the curved top portion 304 and the plane containing the central axis 310, and point B is the intersection between the edge of the bottom opening of the curved top portion 304 and the same plane containing the central axis 310. Unlike the nozzle 234 shown in fig. 2C, the angle α between the straight line connecting the point a and the point B and the central axis 310 is not a fixed angle (e.g., 35 degrees in fig. 2C) determined by the crystal plane of the semiconductor nozzle layer 308. In contrast, when the funnel shaped nozzle 304 is manufactured, the angle α of the funnel shaped nozzle 304 can be designed by changing the process parameters. In some embodiments, the angle α of the funnel shaped nozzle 304 may be between 30-40 degrees. In some embodiments, the angle α of the funnel shaped nozzle 304 may be greater than 40 degrees.

As shown in fig. 3A, the curved top 304 of the funnel-shaped nozzle 302 is different from a circular lip that results from the natural rounding or tapering of the recess walls that occurs during the formation of the cylindrical recess in the base plate.

First, the amount of taper exhibited by the curved top 304 of the funnel-shaped recess 302 is much greater than any taper that may be inherently present due to manufacturing inaccuracies (e.g., etching of a substrate through a straight-walled photoresist mask). For example, the taper angle of the side wall of the funnel-shaped nozzle is about 30 to 40 degrees. The vertical extent of the curved top 304 may be several tens of microns (e.g., 50-75 microns). The width of the top opening of the curved top 304 may be 100 microns or more and may be 3 or 4 times the width of the bottom opening of the curved top 304. In contrast, the taper or rounding that exists near the top opening of the cylindrical recess due to manufacturing defects and/or inaccuracies is typically less than 1 degree. The natural tapering or rounding also has much smaller height and width variations (e.g., in the nanometer or less than 1-2 micron range) than those present in the funnel-shaped nozzles described in this specification.

Fig. 3B is a top view of a funnel-shaped nozzle, such as the nozzle 302 shown in fig. 3A. As shown in fig. 3B, the top opening 312 and the bottom opening 314 of the funnel-shaped nozzle 302 are both circular and concentric. There is no discontinuity throughout any portion of the side surface 316 of the nozzle 302. The width of the top opening 312 is at least 3 times the width of the bottom opening 214 of the nozzle 302. In some embodiments, the top opening 312 of the nozzle 302 is fluidly connected to the pumping chamber above the funnel-shaped nozzle 302, and the boundaries of the pumping chamber define the boundaries of the top opening 312 of the funnel-shaped nozzle 302. Fig. 3C shows a printhead flow path 318 with a funnel-shaped nozzle 302.

Although fig. 3B shows a funnel-shaped nozzle having a circular cross-sectional shape throughout its depth, other cross-sectional shapes are possible. The cross-sectional shape of the straight-walled bottom of the funnel-shaped nozzle may be oval, square, rectangular or other polygonal shape. The curved top of the funnel-shaped nozzle will have a similar cross-sectional shape as the bottom of the straight wall. However, as the side surfaces of the curved top extend further away from the straight wall bottom toward the top opening of the curved top, the corners (if any) in the cross-sectional shape of the curved top are gradually eliminated or smoothed. The exact shape of the cross-section of the curved top is determined by the manufacturing steps and the material used to form the funnel-shaped nozzle.

For example, in some embodiments, a funnel-shaped nozzle having a curved top that smoothly connects to a straight-walled bottom may have a square horizontal cross-sectional shape. In such an embodiment, the center-side profile of the nozzle is the same as that shown in fig. 3A. However, the funnel-shaped nozzle will have four converging curved side surfaces and the intersections between adjacent curved side surfaces are four smooth curved lines converging towards the bottom outlet of the nozzle and smoothly transition to four straight parallel lines in the straight bottom of the nozzle. In addition, the intersection between adjacent curved side surfaces is smoothly rounded, such that the four curved side surfaces form part of a single smooth side surface in the top of the funnel-shaped nozzle.

The printhead body may be fabricated by forming features in various layers of semiconductor material and attaching the layers together to form the body. Flow path features such as pumping chambers and ink inlets to the nozzles can be etched into the substrate using conventional semiconductor processing techniques, as described in U.S. patent application No. 10/189947 filed on 7/3/2002. The nozzle layer and the flow path module together form a printhead body through which ink flows and from which ink is ejected. The shape of the nozzle through which the ink flows can affect the resistance to ink flow. By forming the funnel-shaped nozzle described in the present application, a smaller flow resistance, a higher jetting frequency, a lower driving voltage and/or a better jetting straightness can be achieved. The processing techniques described herein also allow for good uniformity and efficiency of nozzle arrays having the desired size and spacing.

Fig. 4A-4F illustrate a method of making a funnel-shaped nozzle having a curved top portion smoothly connected to a straight-walled bottom portion, such as the funnel-shaped nozzle shown in fig. 3A-3C.

To form the funnel-shaped nozzle, first, a patterned photoresist layer is formed on a top surface of a semiconductor substrate, wherein the patterned photoresist layer includes an opening having a curved side surface smoothly connected to an exposed top surface of the patterned photoresist layer. For example, an opening around the z-axis will have side surfaces that are curved in the z-direction and azimuthal direction. The shape of the opening will determine the cross-sectional shape of the funnel-shaped nozzle in a plane perpendicular to the central axis of the funnel-shaped nozzle. The size of the opening is approximately the same (e.g. 35 microns) as the bottom opening of the funnel-shaped nozzle. In the example shown in fig. 4A-4F, the openings are circular and the funnel-shaped nozzle used for manufacture has a circular horizontal cross-section over the entire depth of the nozzle.

To form the patterned photoresist layer, a resist reflow process may be used. As shown in fig. 4A, a uniform photoresist layer 402 is applied to a planar top surface 404 of the substrate. The substrate may be a semiconductor substrate 406 (e.g., a silicon wafer). The semiconductor substrate 406 may be a substrate having one of several crystal orientations, such as a silicon <100> wafer, a silicon <110> wafer, or a silicon <111> wafer. The thickness of the photoresist layer 402 affects the final curvature of the curved side surface of the opening in the photoresist layer and thus the curved side surface of the funnel-shaped nozzle. A thicker photoresist layer is typically applied to obtain a larger radius of curvature of the curved side surface of the funnel-shaped nozzle.

In this example, the initial thickness of the uniform photoresist layer 402 is about 10-11 microns (e.g., 11 microns). In some embodiments, more than 11 microns of photoresist may be applied on the planar top surface 404 of the semiconductor substrate 406. After the processing step, a thickness of photoresist may be maintained on the substrate to provide the funnel-shaped recess with the desired depth. Examples of photoresists that may be used include, for example, photoresist compositions prepared from

AZ9260, AZ9245, AZ4620 and other positive photoresists manufactured by GmbH. The thickness of the semiconductor substrate 406 is equal to or greater than the desired depth of the funnel-shaped nozzle to be manufactured. For example, the substrate 406 shown in fig. 4A may be an SOI wafer having a silicon layer 403 of about 50 microns, the silicon layer 403 being attached to a handle layer 407 via a thin oxide layer 405. Another thin oxide layer 401 may cover the silicon layer 403. For example, the thin oxide layer 401 may be about 1 micron. As shown in fig. 4A, a first photolithography and etch step may form an opening 409 having a first width 411 in the thin oxide layer 401. The photoresist used to define the opening 409 may be a more precise thin non-reflowable resist. The oxide in the thin oxide layer 401 may also have a high selectivity to the Bosch etch used to form the opening 409. The selectivity between the non-reflowed resist and the substrate is expected to be similar to the selectivity between the reflowed resist and the substrate, e.g., less than 100: 1. In some embodiments, first width 411 is less than second width 413 by about 1 μm. The uniform photoresist layer 402 also fills the opening 409. Alternatively, the substrate 406 may be a thin silicon layer attached to the indicator layer by an adhesive layer or van der waals forces.

As shown in fig. 4B, after the uniform photoresist layer 402 is applied to the planar top surface 404 of the semiconductor substrate 406, the uniform photoresist layer 402 is patterned to create an initial opening 408 having a second width 413 and one or more vertical sidewalls 410. The second width 413 is greater than the first width 411. In some embodiments, the second width 413 may be about 1 μm greater than the first width 411. The stepper may precisely align opening 408 with opening 409. For example, the stepper may store information about the center of the opening 409 defined in the thin oxide layer 401 and match it to the center of the initial opening 408 during the lithographic process that created the initial opening 408. In this example, a circular opening is created in the uniform photoresist layer 402 and the sidewall of the circular opening is a single curved surface that is perpendicular to the planar top surface 412 of the uniform photoresist layer 402 and the planar top surface 404 of the semiconductor substrate 406. The diameter of the opening 411 determines the diameter of the bottom opening of the funnel-shaped nozzle to be manufactured. In this example, the diameter of the initial circular opening 411 may be about 85-95 microns (e.g., 90.5 microns). Patterning of the uniform photoresist layer 402 may include standard UV or light exposure and photoresist development processes under a photomask to remove portions of the photoresist layer exposed to light.

After the initial opening 408 is formed in the uniform photoresist layer 402, the photoresist layer 402 is heated to about 160 to 250 degrees celsius until the photoresist material in the layer 402 softens. When the photoresist material in patterned photoresist layer 402 softens under thermal treatment, the photoresist material will begin to reflow and reshape itself under the influence of the surface tension of the photoresist material, particularly in the region near the top edge 414 of opening 408. The surface tension of the photoresist material causes the surface profile of the opening 408 to pull back and round. As shown in fig. 4C, the top edge 414 of the opening 408 is rounded under the influence of surface tension. The opening in the resist 413 is substantially unchanged from the reflow.

In some embodiments, the photoresist layer 402 is heated in a vacuum environment to achieve reflow of the photoresist layer 402. By heating the photoresist layer 402 in a vacuum environment, the surface of the photoresist layer 402 is smoother and no micro-bubbles are trapped inside the photoresist material. This will result in better surface smoothness in the final nozzle produced.

After the desired shape of the opening 408 is obtained, the photoresist layer 402 is cooled. Cooling may be accomplished by removing a heat source or active cooling. The cooling can also be carried out in a vacuum environment to ensure better surface properties of the funnel-shaped nozzle to be manufactured. By cooling the photoresist layer 402, the photoresist layer 402 re-hardens, and the surface profile of the opening 408 retains its shape during the hardening process, and the top edge 414 of the opening 408 remains rounded at the end of the re-hardening process.

Once the patterned photoresist layer 402 is hardened, etching of the substrate 406 may begin. The funnel-shaped recess is produced by a two-step etching process. First, a straight-walled recess is produced in a first etching process. Then, the straight-walled recess is changed in a second etching process. In the second etching process, the initially formed straight-walled recess is deepened to form a straight-walled bottom of the funnel-shaped recess. At the same time, the second etching process gradually expands the initially formed straight-walled recess from the top to form a curved top of the funnel-shaped recess.

As shown in fig. 4C, an initial straight-walled recess 416 is created through opening 409 during a first etch. In other words, the edges of the oxide in the thin oxide layer 401 define the boundaries of the recesses 416, rather than the reflowed resist 402. The first etching process may be, for example, a Bosch process. In a first etching process, straight-walled recesses 416 are created, the depth of which is slightly less than the final desired depth of the funnel-shaped recess to be fabricated (e.g., 1-15 microns less). For example, for funnel-shaped recesses having a total depth of 50-80 microns, the straight-walled recesses 416 produced during the first etch may be 49-79 microns. Although there may be a slight fan-shaped pattern on the side profile 418 of the straight-walled recess 416, this small variation (e.g., 1 or 2 degrees) is small compared to the overall dimensions of the straight-walled recess 416 (e.g., 35 microns wide and 45-75 microns deep).

During the first etching process, the straight-walled recess 416 has substantially the same cross-sectional shape and size as the region surrounded by the opening 409 in a plane parallel to the top surface 404 of the semiconductor substrate 406. As shown in fig. 4D, the etchant used in the first etching process removes very little of the photoresist layer 402 as compared to the device layer 403 of the semiconductor substrate 406 exposed through the opening 409 in the thin oxide layer 401. Thus, at the end of the first etch process, the surface profile of the patterned photoresist layer 402 remains substantially unchanged. For example, the selectivity between the device layer 403 and the photoresist layer 402 during the first etch process may be 100: 1.

After the initial straight-walled recess 416 is formed in the semiconductor substrate 406 by the first etching process, a second etching process may be initiated to convert the initial straight-walled recess 416 shown in fig. 4C into the desired funnel-shaped recess 420 shown in fig. 4D.

As shown in fig. 4D, the semiconductor substrate 406 and the patterned photoresist layer 402 are exposed to a dry etch from a vertical direction (e.g., a direction perpendicular to the planar top surface 404 of the substrate 406 in fig. 4D). The etchant used in the dry etching process may have a comparable etch rate for the photoresist and the semiconductor substrate 406. For example, the selectivity of the dry etching between the photoresist and the semiconductor substrate may be 1: 1. In some embodiments, the dry etch is performed at high plate power (e.g., greater than 400W) using a CF4/CHF3 and O2 gas mixture.

During dry etching, the surface profile of the photoresist layer 402 recedes in the vertical direction under bombardment of the etchant as the etching process continues. Due to the curved profile 414 at the top edge of the opening 408 in the photoresist layer 402, the surface of the thin oxide layer 401 below the thinnest portion of the photoresist layer 402 is exposed to the etchant first, as compared to other portions of the substrate surface below the photoresist layer 402. In other words, the thin oxide layer 401 is etched. Portions of the semiconductor surface exposed to the etchant are also gradually etched away. As shown in fig. 4D, the dashed lines indicate that the surface profile 414 of the photoresist layer 402 and the semiconductor substrate 406 gradually recedes under the bombardment of the etchant.

As shown in fig. 4D, the region 422 below the edge of the opening 409 in the thin oxide layer 401 is etched, and the surface of the device layer 403 expands in the lateral direction. The expansion of the side surfaces 418 of the recess 416 becomes curved side surfaces 424 of the curved top of the funnel-shaped recess 420 formed in the semiconductor substrate 406.

As the dry etching continues to expand the side surfaces 418 of the recesses 416 in the lateral direction, the dry etching also deepens the recesses 416 in the vertical direction. The deepening of the recess 416 creates a straight-walled bottom of the funnel-shaped recess 420. The additional deepening creates straight wall portions several microns deep. The side surfaces 426 of the straight wall bottom are perpendicular to the planar top surface 404 of the semiconductor substrate 406. Since the lateral expansion of the side surface 424 of the recess 420 is gradually reduced from the top to the bottom, the curved side surface 424 of the curved top smoothly transitions to the vertical side surface 426 of the straight wall bottom. The boundary of the top opening of the funnel-shaped recess 420 is defined by the edge where the photoresist meets the surface of the thin oxide layer 401.

The dry etch may be timed and stopped once the desired depth of the funnel-shaped recess 420 is reached. Alternatively, the dry etching is timed and stopped once the desired surface profile of the curved portion of the funnel-shaped recess 420 is obtained.

In some embodiments, if the semiconductor substrate has a nozzle layer of a desired thickness, dry etching may be continued until the etch is through the entire thickness of the semiconductor substrate and the funnel-shaped nozzle is completely formed. In some embodiments, the semiconductor substrate may be etched, ground, and/or polished from the backside until the funnel-shaped recess opens from the backside to form the funnel-shaped nozzle.

The photoresist 402 is removed and fig. 4E shows the complete funnel-shaped recess 428 open at the bottom. After forming the funnel-shaped nozzle 428, the nozzle layer 429 may be attached to other layers of a fluid ejection unit, such as the fluid ejection unit 430 shown in fig. 4F. In some embodiments, the funnel-shaped nozzle 428 is one of an identical array of funnel-shaped nozzles, and each of the identical array of funnel-shaped nozzles belongs to an independently controllable fluid ejection unit 430. In some embodiments, the fluid ejection unit includes a piezoelectric actuator assembly supported on the top surface of the semiconductor substrate 406 and including a flexible membrane sealing a pumping chamber fluidly connected to a funnel-shaped nozzle 428. Each actuation of the flexible membrane is operable to eject a fluid droplet through the straight-walled bottom of the funnel-shaped nozzle 428, and the volume enclosed by the curved top is three or four times the size of the fluid droplet.

Fig. 5A and 5B show images of two funnel-shaped recesses (e.g., recess 502 and recess 504) made using the process shown in fig. 4A-4F.

In different embodiments, the size of the funnel-shaped recess may be different. As shown in FIG. 5A, the bottom 506 of the funnel-shaped recess 502 has a depth of about 2-5 microns, while the curved top 508 of the funnel-shaped recess 502 has a depth of about 25-28 microns. When a funnel-shaped nozzle is generated from the funnel-shaped recess 502, the substrate may be ground and polished from the bottom so that the straight wall portion 506 has a desired depth. As shown in FIG. 5A, the diameter of the straight-walled bottom 506 is substantially uniform (with a variation of less than 0.5 microns for a 20 micron diameter) in a plane perpendicular to the central axis of the recess 502. The bottom opening of the curved top 508 is smoothly connected to the top opening of the straight-walled bottom 506. The diameter of the top opening of the recess 502 is in the range of 96 microns, about 5 times the diameter of the straight-walled bottom 506. The spacing of the curved tops 508 spreading from bottom to top may be defined by the width of the curved tops 508 at half the height of the curved tops 508. In this example, the width at half height of the curved top is about 27 microns. A descender 510 is located above the recess 502.

The portion of the funnel-shaped recess 502 within the dashed rectangular box region is shown in fig. 5B. The image in fig. 5B is rotated by 180 °, and at higher magnification, the recess 502 has virtually no straight-walled portion.

Fig. 6A shows a graph of maximum, minimum and average funnel nozzle sizes fabricated on two wafers using the process outlined in fig. 4A-4F. By way of comparison, fig. 6B shows a plot of the maximum, minimum and average funnel nozzle sizes fabricated on fifteen wafers using another process in which the reflowed photoresist has an initial opening that is smaller than the opening defined in the thin oxide layer. Using another process, the edge of the reflowed resist defines the nozzle boundary of the straight-walled recess formed during the first etching process shown in fig. 4C. Curve 602 in FIG. 6A shows the maximum funnel nozzle size, which falls mostly between 22-23 microns. In contrast, curve 608 in fig. 6B shows a large variation in the maximum funnel nozzle size, which is between about 19 and 22.5 microns. Curve 604 in fig. 6A shows the minimum funnel nozzle size, which falls mostly between 21.5-22.4 microns. In contrast, curve 610 in fig. 6B shows a significantly larger variation in the minimum funnel nozzle size, which is between about 17 and 21.5 microns. Curve 606 in fig. 6A shows the average funnel nozzle size with much less variation than curve 612 in fig. 6B.

Based on empirical data, such as that shown in fig. 6A and 6B, the diameter of the funnel holes varied more than the width of KOH nozzles, such as those shown in fig. 2A, where the nozzles had a straight, sloped profile. A small portion of the funnel holes may be approximately (1-3 μm) smaller than the population. Nozzle size variations can result in print line width variations, so a nozzle plate with too much variation may have to be scrapped. For nozzle diameter variation specifications of ± 1.5 μm, a large (e.g. 25%) die yield loss may result. The process outlined in fig. 4A-4F accounts for the variability that may be caused by the reflow process, since no dimensional change is observed on straight holes etched into the silicon wafer using non-reflowed resist. The modification to the funnel nozzle process results in a funnel nozzle with reduced orifice size variation, as shown in fig. 6A.

Fig. 7A shows a plot 702 of the standard deviation of the nozzle width fabricated using the process shown in fig. 4A-4F. The standard deviation for most nozzles is about 0.1 microns. In contrast, fig. 7B shows a plot 704 of the standard deviation of nozzle width fabricated using another process in which the edges of the reflowed resist define the nozzle boundaries of the straight-walled recesses formed during the first etching process shown in fig. 4C. The standard deviation in curve 704 is typically greater than 0.2 microns.

A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Exemplary methods of forming the foregoing structures have been described. However, other processes may be substituted for those described to achieve the same or similar results. Accordingly, other embodiments are within the scope of the following claims.

Claims

1. A method of manufacturing a nozzle, the method comprising:

forming a first opening having a first width in a top layer of a substrate, wherein the substrate comprises the top layer and an underlying second layer of a different material than the top layer;

forming a patterned layer on a top surface of a substrate such that the patterned layer is on top of a top layer of the substrate, the patterned layer including a second opening spanning a first opening in the top layer, the second opening having a second width greater than the first width;

reflowing the patterned layer to form a curved side surface that terminates at a top surface of a substrate, wherein reflowing the patterned layer comprises softening the patterned layer by heating until a top edge of the second opening is rounded under the influence of surface tension, and after softening by heating, re-hardening the patterned layer while the top edge of the second opening remains rounded;

etching a second layer of the substrate through a first opening in a top layer of the substrate to form a straight-walled recess in the second layer, wherein an outer edge of the first opening in the top layer defines a boundary of the straight-walled recess, the straight-walled recess having the first width, a bottom surface, and a side surface substantially perpendicular to a top surface of the substrate; and

after forming the straight-walled recess, the curved side surface of the patterned layer, the top layer of the substrate, and the second layer of the substrate are etched while the inner surface of the straight-walled recess is exposed to the etching, wherein the etching transforms the straight-walled recess into a funnel-shaped recess comprising curved side walls gradually smoothly connecting lower portions of the straight walls of the recess or terminating at the bottom surface.

2. The method of claim 1, wherein the second opening is about 1 μ ι η larger than the first opening.

3. The method of claim 2, wherein the patterned layer on the top surface of the substrate having the first opening is precisely aligned using a stepper.

4. The method of claim 1, wherein the first opening is formed by etching with a thin, unreflowed resist.

5. The method of claim 4, wherein the substrate is a semiconductor substrate and the second layer is an oxide layer having a high selectivity to a Bosch etch process.

6. The method of claim 1, wherein the patterned layer deposited on the top surface of the substrate has a thickness of at least 10 microns.

7. The method of claim 1, wherein softening the patterned layer by heating further comprises:

the patterned layer having the second openings formed therein is heated in a vacuum environment until the material in the patterned layer reflows under the influence of surface tension.

8. The method of claim 1 wherein heating the patterned layer comprises heating the patterned layer to a temperature of 160-250 degrees celsius.

9. The method of claim 1, wherein re-hardening the patterned layer comprises cooling the patterned layer while a top edge of the second opening remains rounded.

10. The method of claim 1, wherein the width of the top opening of the curved sidewall is at least four times the width of the bottom opening of the curved sidewall.

11. The method of claim 1, wherein etching the top surface of the substrate to form the straight-walled recess comprises etching the top surface of the substrate through an opening in the patterned layer using a Bosch process.

12. The method of claim 1, wherein the etching that forms the funnel-shaped recess has substantially the same etch rate for the patterned layer and the substrate.

13. A method of manufacturing a nozzle, the method comprising:

reflowing the patterned layer to form curved side surfaces terminating at a top surface of a substrate;

after forming the straight-walled recess, etching the curved side surface of the patterned layer, the top layer of the substrate, and the second layer of the substrate while an inner surface of the straight-walled recess is exposed to the etching, wherein the etching transforms the straight-walled recess into a funnel-shaped recess comprising curved side walls gradually smoothly connecting lower portions of the straight walls of the recess or terminating at the bottom surface;

wherein the first opening in the patterned layer has a circular cross-sectional shape in a plane parallel to the exposed top surface of the patterned layer.

14. A method of manufacturing a nozzle, the method comprising:

the funnel-shaped recess has a circular cross-sectional shape in a plane parallel to a top surface of the substrate.

15. A method of forming a plurality of nozzles using the method of claim 1, wherein the standard deviation of the nozzle widths of the plurality of nozzles is less than 0.15 microns.

16. The method of claim 1, wherein the recess extends all the way through the top layer.

17. A method of manufacturing a nozzle, the method comprising:

after forming the straight-walled recess, the curved side surface of the patterned layer, the top layer of the substrate, and the second layer of the substrate are etched while the bottom surface and the side surfaces of the straight-walled recess are exposed to the etch, wherein the etch transforms the straight-walled recess into a funnel-shaped recess comprising curved side walls gradually smoothly connecting lower portions of the straight walls of the recess or terminating at the bottom surface.

18. The method of claim 17, wherein the second opening is about 1 μ ι η larger than the first opening.

19. The method of claim 18, wherein the patterned layer on the top surface of the substrate having the first opening is precisely aligned using a stepper.

20. The method of claim 17, wherein the first opening is formed by etching with a thin, unreflowed resist.

21. The method of claim 20, wherein the substrate is a semiconductor substrate and the second layer is an oxide layer having high selectivity to a Bosch etch process.

22. The method of claim 17, wherein reflowing the patterned layer comprises:

softening the patterned layer by heating until the top edge of the second opening becomes rounded under the influence of surface tension; and

after softening by heating, the patterned layer is re-hardened while the top edge of the second opening remains rounded.

23. The method of claim 22, wherein the patterned layer deposited on the top surface of the substrate has a thickness of at least 10 microns.

24. The method of claim 22, wherein softening the patterned agent layer by heating further comprises:

heating the patterned layer having the second openings formed therein in a vacuum environment until the material in the patterned layer reflows under the influence of surface tension.

25. The method of claim 22 wherein heating the patterned layer comprises heating the patterned layer to a temperature of 160-250 degrees celsius.

26. The method of claim 22, wherein re-hardening the patterned layer comprises cooling the patterned layer while a top edge of the second opening remains rounded.

27. The method of claim 17, wherein the width of the top opening of the curved sidewall is at least four times the width of the bottom opening of the curved sidewall.

28. The method of claim 17, wherein etching the top surface of the substrate to form the straight-walled recess comprises etching the top surface of the substrate through an opening in the patterned layer using a Bosch process.

29. The method of claim 17, wherein the etching that forms the funnel-shaped recess has substantially the same etch rate for the patterned layer and the substrate.

30. The method of claim 17, wherein the etching to form the funnel-shaped recess comprises using CF₄/CHF₃Etching of the gas mixture.

31. The method of claim 17, wherein the first opening in the patterned layer has a circular cross-sectional shape in a plane parallel to the exposed top surface of the patterned layer.

32. The method of claim 17, wherein the funnel-shaped recess has a circular cross-sectional shape in a plane parallel to a top surface of the substrate.

33. A method of forming a plurality of nozzles using the method of claim 17, wherein the standard deviation of the nozzle widths of the plurality of nozzles is less than 0.15 microns.

34. The method of claim 17, wherein the recess extends all the way through the top layer.

35. A method of manufacturing a nozzle, the method comprising:

etching a second layer of the substrate through a first opening in a top layer of the substrate to form a straight-walled recess in the second layer, wherein an outer edge of the first opening in the top layer defines a boundary of the straight-walled recess, the straight-walled recess having the first width, a bottom surface, and a side surface substantially perpendicular to a top surface of the substrate, the second layer of the substrate underlying the top layer of the substrate; and

36. The method of claim 35, wherein the second opening is about 1 μ ι η larger than the first opening.

37. A method of manufacturing a nozzle, the method comprising:

forming a first opening having a first width in a top layer of a substrate;

forming a patterned layer on a top surface of a substrate such that the patterned layer is located on a top layer of the substrate, the patterned layer including a second opening spanning a first opening in the top layer, the second opening having a second width greater than the first width;

etching a second layer of the substrate through a first opening in a top layer of the substrate to form a recess in the second layer, the recess extending from a bottom surface of the recess to a top surface of the substrate and having a substantially constant width; and

after forming the recess, the curved side surfaces of the patterned layer, the top layer of the substrate, and the second layer of the substrate are etched while the bottom surface of the recess is exposed to the etching, wherein the etching forms the curved sidewalls of the recess such that the recess is wider at the top surface of the substrate than at the bottom surface of the recess.

38. The method of claim 37, comprising aligning the patterned layer on the top surface of the substrate using a stepper.

39. The method of claim 37, wherein forming the first opening comprises etching the first opening using a non-reflowed resist.

40. The method of claim 37, wherein the substrate is a semiconductor substrate and the second layer is an oxide layer having a high selectivity to a Bosch etch process.

41. The method of claim 37, wherein etching the top surface of the substrate to form the recess comprises etching the top surface of the substrate through an opening in the patterned layer using a Bosch process.

42. The method of claim 37, wherein reflowing the patterned layer comprises:

softening the patterned layer by heating until a top edge of the second opening becomes rounded; and

43. The method of claim 42, softening the patterned layer comprising heating the patterned layer having the second openings formed therein in a vacuum environment.

44. The method of claim 43, comprising heating the patterned layer having the second opening until the patterned layer reflows.

45. The method as recited in claim 43, including heating said patterned layer to a temperature of 160-250 degrees Celsius.

46. The method of claim 42, wherein re-hardening the patterned layer comprises cooling the patterned layer while a top edge of the second opening remains rounded.

47. The method of claim 37, wherein the etch that forms the recess has substantially the same etch rate for the patterned layer and the substrate.

48. The method of claim 37, comprising using CF₄/CHF₃The gas mixture etches a second layer of the substrate.

49. The method of claim 37, wherein the second width is about 1 μm greater than the first width.

50. The method of claim 37, wherein the patterned layer has a thickness of at least 10 μm.

51. A method of manufacturing a nozzle, the method comprising:

etching a second layer of the substrate through a first opening in a top layer of the substrate to form a recess in the second layer, wherein an outer edge of the first opening in the top layer defines a boundary of the recess, the recess extending from a bottom surface of the recess to a top surface of the substrate and having a substantially constant width; and

52. The method of claim 51, wherein reflowing the patterned layer comprises:

53. The method of claim 52, softening the patterned layer comprising heating the patterned layer having the second openings formed therein in a vacuum environment.

54. The method of claim 53, comprising heating the patterned layer having the second opening until the patterned layer reflows.

55. The method as recited in claim 53, comprising heating the patterned layer to a temperature of 160-250 degrees Celsius.

56. The method of claim 52, wherein re-hardening the patterned layer comprises cooling the patterned layer while a top edge of the second opening remains rounded.